Abstract

Even in the early stages of their development, tumours are not simply a homogeneous grouping of mutant cells; rather, they develop in tandem with normal tissue cells, and also recruit other cell types including lymphatic cells and the endothelial cells required for the development of a blood supply. It has been repeatedly seen that macrophages form a significant proportion of the tumour mass, and that they can have a variety of effects upon the tumour, leading to a delicate balance between growth promotion and inhibition. This paper develops a model for the early, avascular growth of a tumour, concentrating on the inhibitory effect of macrophages due to their cytolytic activity. It is shown that such an immune response is not sufficient to prevent growth, due to it being a second-order process with respect to the density of the tumour cells present. However, the presence of macrophages does have important effects on the tumour composition, and the authors perform a detailed bifurcation analysis of their model to clarify this. An extended model is also considered which incorporates addition of exogenous chemical regulators. In this case, the model admits the possibility of tumour regression, and the therapeutic implications of this are discussed.